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Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximation

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Date
2017
Collection title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Link to item file
https://hal.archives-ouvertes.fr/hal-01623403
Dewey
Probabilités et mathématiques appliquées
Sujet
Kernel rule; nonparametric estimation; cell division; deconvolution; Growth-fragmentation
URI
https://basepub.dauphine.fr/handle/123456789/17536
Collections
  • CEREMADE : Publications
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Author
Hoang, Van Ha
32 Laboratoire Paul Painlevé - UMR 8524 [LPP]
Pham Ngoc, Thanh Mai
40 Laboratoire de Mathématiques d'Orsay [LM-Orsay]
Rivoirard, Vincent
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Tran, Viet Chi
32 Laboratoire Paul Painlevé - UMR 8524 [LPP]
Type
Document de travail / Working paper
Item number of pages
29
Abstract (EN)
We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We address here the problem of nonparametric estimation of the kernel ruling the divisions based on the eigenvalue problem related to the asymptotic behavior in large population. This inverse problem involves a multiplicative deconvolution operator. Using Fourier technics we derive a nonparametric estimator whose consistency is studied. The main difficulty comes from the non-standard equations connecting the Fourier transforms of the kernel and the parameters of the model. A numerical study is carried out and we pay special attention to the derivation of bandwidths by using resampling.

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